Quaresma, 30, played for Porto between 2004 and 2008 and was a free agent having most recently been with Al Ahli in Dubai.
"I am happy to return to a home I know well, where I can feel the love and faith of the fans," said Quaresma in a statement on the club's official website.
More than 10,000 supporters attended an open training session on New Year's Day in which Quaresma took part. The winger has also played for Sporting Lisbon, Barcelona, Inter Milan, Chelsea and Besiktas.
Defending Portuguese champions Porto currently sit second in their domestic league, level on points with leaders Sporting and third-placed Benfica.
They were knocked out of the UEFA Champions League at the group stage but will play in the knockout phase of the UEFA Europa League, a competition they won in 2011.